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SAN FRANCISCO — Second baseman Marco Scutaro is staying in San Francisco, right where he wanted to be.

The NL championship series MVP agreed to a $20 million, three-year contract with the Giants late Tuesday. Vice president of baseball operations Bobby Evans said only a physical was left to finalize the deal.

“He was a priority from Day One,” Evans said. “He was a key part of our 2012 success and served as a tremendous veteran presence.”

Earlier in the evening, Scutaro had been weighing a two-year contract offer that included a vesting option — but he was seeking a three-year deal to remain with the World Series champions. The Giants and Scutaro’s representatives met Tuesday at the winter meetings in Nashville, Tenn.

The 37-year-old Scutaro batted .362 with three homers and 44 RBIs in 61 regular-season games with the Giants after he was acquired in a July 27 trade with Colorado. He frequently said how much he enjoyed playing for San Francisco and that he hoped he would return.

The Giants suddenly have quite a familiar roster returning after making two big moves in as many days to keep their own free agents. On Monday, center fielder Angel Pagan agreed to a $40 million, four-year contract.

Retaining Affeldt, Pagan and Scutaro were among the top priorities for Sabean and Evans this offseason.

Giants CEO Larry Baer considered it a productive winter meetings — and offseason so far — for his busy club after already re-signing Affeldt last month. Winning the World Series for the second time in three seasons put San Francisco behind on its offseason plan again, although everyone in the front office would say that’s a great problem to have.